Chapters
- 018 demonstrations
Foundations and Notation
Measure a profile, compress a table, score a forecast, trace a change, and know how much data is enough.
- 028 demonstrations
Approximation and Expressivity
Construct curves, count pieces, and separate three obstacles.
- 038 demonstrations
Optimization and Training Dynamics
Inspect stable steps, noisy gradients, adaptive moments, schedules, curvature limits and batch size.
- 048 demonstrations
Generalization and Implicit Bias
Separate repeated-fit uncertainty, bounds, interpolation, and solution choice.
- 058 demonstrations
Symmetry and Geometric Inductive Bias
Specify what should stay fixed and what should transform.
- 068 demonstrations
Convolutional and Multiscale Models
Inspect filter conventions, aliases, localized changes, residual maps, and the cost of scale.
- 078 demonstrations
Recurrent and State-Space Models
Track decay, Jacobian products, gated retention, and convolutional memory.
- 088 demonstrations
Attention and Transformers
Follow information through attention, sampling, position, and growing context.
- 098 demonstrations
Graph and Geometric Deep Learning
Follow relationships, audit bridges and test what local labels miss.
- 108 demonstrations
Latent, Adversarial, and Flow Models
Integrate hidden variation, inspect bounds and measure missing modes.
- 118 demonstrations
Diffusion, Score, and Transport-Based Generation
Track noise, read scores and compare two reverse journeys.
- 128 demonstrations
Continuous-Depth and Implicit Models
Separate equilibria, convergence and numerical artifacts.
- 138 demonstrations
Scientific ML and Operator Learning
Test laws, conditions and trajectory evidence separately.
- 148 demonstrations
Bayesian Deep Learning and Uncertainty
Update a belief, separate uncertainties, and check a forecast.
- 158 demonstrations
Robustness, OOD, and Causality
Check how a conclusion changes with inputs, populations and interventions.
- 168 demonstrations
Scaling Laws, In-Context Learning, and Abstract Foundations
Distinguish resources, examples and the objective being rewarded.
- 178 demonstrations
The Mathematics of Truth, Error, and Abstention
Separate what was seen, what is supported, and what can responsibly be answered.
Notebooks on GitHub
Every chapter has a Jupyter notebook with the same figures and results, plus optional Python cells that reproduce each calculation.
Examples use book values or disclosed illustrative parameters. A mathematical illustration is not evidence about a specific AI product or a substitute for checking a factual claim.